The 18-year-old defender was playing in a practice match for Ireland when the freak injury occurred and he was treated on the pitch before being taken to Mater Hospital in Dublin.
Duffy had emergency surgery to repair a damaged artery that was causing internal bleeding. The teenager has since been moved from intensive care to a high dependency ward.
"I would like to thank (team doctor) Dr. Alan Byrne and (team consultant) Prof. John O'Byrne for their quick reaction to Shane's serious injury," said Ireland manager Giovanni Trapattoni.
"As time was critical, had they not acted as they did, Shane's life could have been in more danger than it already was," he added on the Everton website.
"On behalf of the FAI, I would also like to praise Prof. Gerry McEntee for conducting the emergency operation and ensuring that Shane was given the best possible attention.
"Shane is very lucky and we wish him a speedy recovery."
O'Byrne said he believed the injury would not occur in another 100 years of football, such was its unusual nature.
Duffy, who played for Northern Ireland's under-21 side before switching allegiance to Ireland, made his Everton debut against AEK Athens in the Europa League in December.
